Question: Rewrite the following equation in logarithmic form. 1 = 10 0 1=10\^ {{0}} Rewrite the following equation in exponential form. $ \log_{5}{\left(\dfrac{1}{25}\right)}=-2 $
Solution: The inverse relationship of exponents and logarithms For $m>0$ and $b>0, b\neq 1$, we have the following relationship: b q = m { b\^{{ q}}}}= m if and only if $ \log_{ b }{ m}=D q$ Converting the exponential equation So 10 0 = 1 \, {{10}\^{ {0}}}}= {1}\, implies that $\,\log_{ {10}}({ {1}})=D {0}$. This can also be written as $\log(1)=0$ [What happened to the base?] Converting the logarithmic equation Similarly $\, \log_{ 5}\left({{\dfrac{1}{25}}}\right)=-2}\,$ implies that 5 − 2 = 1 25 \, 5\^{D { {-2}}}={\dfrac{1}{25}}. The logarithmic form of 1 = 10 0 1=10\^ {{0}} is: $\,\log{{(1)}}={0}$ The exponential form of $ \log_{5}{\left(\dfrac{1}{25}\right)}=-2 $ is: 5 − 2 = 1 25 \,5\^{{ {-2}}}=\dfrac{1}{25}